Timber Production Possibilities and Capital Yields from the Norwegian Forest Area

Timber Production Possibilities and Capital Yields from the Norwegian Forest Area

Hans Fredrik Hoen, Tron Eid and Petter Økseter

Hoen, H.F., Eid, T. & Økseter, P. 2001. Timber production possibilities and capital yields from the Norwegian forest area. Silva Fennica 35(3): 249–264.

How intensely should a forest be grown? This is a fundamental question in the process of formulating policy guidelines for the management of a forest area, both at the individual property level as well as at the national level. The question is related to a number of factors; the objective(s) of the forest owner, the productivity of the forestland, the initial growing stock, the accessibility within the forest, assumptions regarding future prices and costs and the required real rate of return. This paper presents an applied analysis with the objective of mapping possible future paths for the growing stock on, and timber harvest from the productive forest area in Norway. The analysis is deterministic. The regeneration strategy is a key factor for the long run development of a forest and is thus given particular attention. The analysis is restricted to deal with timber production only and maximisation of the net present value of the forest area is used as the objective function. The required real rate of return is varied and used as the driving force to fi nd the best (optimal) level of intensity in silvicultural management and thus optimal paths for harvesting and growing stocks.

Keywords timber production possibilities, rate of return, capital yield, forest manage- ment

Authors´ address Agricultural University of Norway, Dept. of Forest Sciences, P.O. Box 5044, N-1432 Ås, Norway

Fax +47 64 948 890 E-mail hans.hoen@isf.nlh.no Received 8 February 2000 Accepted 12 January 2001

1 Introduction

How intensely should a forest be grown? This is a fundamental question in the process of formulat- ing policy guidelines for the management of a forest area, both at the individual property level as well as at the national level. The question is related to a number of factors; the objective(s) of the forest owner, the productivity of the forest- land, the initial growing stock, the accessibility within the forest, assumptions regarding future prices and costs and the required real rate of return (p_r).

The regeneration intensity is fundamental for the long run timber production. When an even- aged stand is established an upper bound on the number of trees per area unit is given for the proceeding rotation. From a biological point of view, a large number of different regenera- tion options are available, from “pure” natural regeneration to intensive treatments of the land including e.g. site preparation, planting, weeding and other measures to control the number and composition of tree species. Regeneration condi- tions and results may vary with vegetation type, altitude, temperature, precipitation, dominating species and species composition in the previous timber rotation. The relation between the total volume production and the number of trees in a stand is one important factor in predictions of future volume production given different intensi- ties in regeneration investments. Growth studies of Norway spruce (Picea abies (L.) Karst.) indi- cate that total volume production is moderately affected by changes in the total number of trees for a wide range of tree numbers (Braastad 1975).

The regeneration lag, i.e. the time from fi nal fell- ing of an existing stand until a new stand is estab- lished, is another vital factor in predictions of long run timber production. An increased regeneration lag will ceteris paribus lead to decreased mean annual volume production for a timber rotation.

The other end of the chain of silvicultural treat- ments constitutes the fi nal harvest. Key factors in this decision relates to expected timber price development, the biological vitality of the stand (i.e. growth and mortality) and ^pr. The forest economic tradition has typically studied questions related to the profi tability of timber production

at stand level, thus assuming that each individual stand can be managed independently of other stands in the forest. The forest planning tradi- tion has typically been occupied with estimating harvest paths based on forest inventory data and growth and yield estimates. The concept of non- declining harvest fl ow has been central in this tradition. Emphasis has been on fi nding manage- ment strategies that could “guarantee” a certain, non-declining, level of harvest. Developments in computer technology have made possible a much more detailed representation for the forest area, compared with the situation only 15 years ago, facilitating analyses with greater richness in underlying assumptions.

Hofstad (1991) reports on an optimal control theory model for the determination of the optimal path from the initial state to an optimal steady state situation. Based on aggregate Norwegian data, he applies a simple logistic growth function, and assumes timber growth to be a function of the inventory. Demand is modelled as a downward sloping function of price, i.e. the value of the harvest is assumed to be a logarithmic function of the quantity supplied. Within this framework Hofstad (l.c.) is able to calculate the optimal harvest path through time and simultaneously determine the optimal level of inventory given the interest rate. An earlier, and similar approach is presented by Lyon and Sedjo (1983). They apply a discrete time optimal control model and solve it by means of a gradient search in order to establish the optimality conditions. The objec- tive function they apply is the sum of consum- ers’ and producers’ surplus, which is maximised subject to the initial conditions and the dynamics of the forestry system. The model treats both the harvesting decision and decisions about the silvicultural investment level endogenously, i.e.

it is capable of simultaneously determining the optimal steady state solution and the optimal path, within a predetermined time period, from the initial state to the steady state.

Nersten et al. (1982) analysed the timber pro- duction potential in Norway. Five different sce- narios were defi ned, with different intensities in silvicultural management as well as different harvest paths. A heuristic algorithm was applied to solve the decision problems numerically. The study was based on sample plot data from the

Norwegian National Forest Inventory, aggregated to fairly few management units.

This analysis quantifi es possible development paths for the productive forest area in Norway, south of Saltfjellet. The main emphasis is put on studying consequences for future timber produc- tion of varying the intensity in the silvicultural management. We assume that the forest will be managed with an even-aged silvicultural regime;

timber production is the only output considered and the analyses are done at forest level. The study is based on a detailed description of a large forest area, thus rendering possible a fairly detailed representation of the variation in key fac- tors in forest management decisions. The paper is organised as follows: The next section fi rst discuss the economics of regeneration briefl y, and then presents the data, assumptions and method- ology of the study. After that, the results from the analysis of timber production potentials on the productive forest area of Norway are presented.

The main uncertainties of the study are discussed and fi nally conclusions are drawn.

2 Material and Methods

2.1 Regeneration Investments

From an economic perspective, the appropriate level of intensity in silvicultural management, such as regeneration, is crucially depending on p_r. The issue have been treated by a number of authors; see e.g. Johansson and Løfgren (1985) or Chang (1983, 1998). Changes in p_r will impact the management of the current growing stock, as well as the level of intensity in regeneration and management of new stands. Forests have the unique attribute of being able to regenerate natu- rally. Given that a naturally regenerated stand, if left unmanaged, at some future point in time will have a positive stumpage value, the net present value of the land will be positive for any strictly positive, p_r. This value represents a pure profi t (economic rent) if the cost of land is set equal to zero. Alternatively, it represents the value of land in timber production when all other input factors are paid at competitive market prices. This (residual) value represents a lower bound on the

value of forestland. If a more intensive manage- ment program is applied, this should generate a higher land value, compared with the ‘no input’

land value, to be defensible economically. We will use a graphical illustration from Svendsrud (1990) to discuss the economically effi cient inten- sity in regeneration investments.

The curve V gives the present value or expecta- tion value, of a timber stand immediately after establishment. V is given as a function of the level of investments, c, in regeneration operations and it is assumed that the investment expenditures are used effi ciently. When c equals zero, this implic- itly means that a stand is established naturally and N gives the present value of this option. Since investments are assumed to occur immediately, we can map c (as an investment cost line) in terms of V as the straight line with a 45° angle starting from origo. Thus the net value of land is V – c.

In Fig. 1 this value increases as regeneration expenditures are incurred. The optimal level of investments is indicated by copt, where marginal revenue equals marginal cost, thus the last unit invested in regeneration obtains a profi tability exactly equal to ^pr. At cmax the level of invest- ments is so high that the net land value is brought down to N, thus no extra profi t is gained by the regeneration efforts. When V intersects with the cost line, the net present value (NPV) of the established stand is zero. In this case the level of Fig. 1. How much should be invested in stand regenera-

tion efforts? (Based on Svendsrud 1990). Explana- tions given in the text.

<– V = f(c) N

C N

V

c_opt c_max

45°

45°

investment is far too high since the value N, i.e.

the pure profi t or land value that could be obtained assuming natural regeneration, is foregone. We implicitly assume that the marginal profi tability of regeneration investments is declining, as can be seen from the proposed curvature of V in Fig. 1. The shape of the curve V (and the size of N) will i.a. be affected by ^pr. An increase in ^pr

will reduce the size of N and make the curvature of V more fl at. At a certain p_r, the slope of V will be less than 1 even when c approaches 0, thus implying natural regeneration to be the best choice.

2.2 Data and Assumptions

The sixth national forest inventory was carried out in Norway in the period from 1986 to 1993 (Statistics of … 1993). The sample plots from this inventory are used to explain the initial state of

the forest area. 24 077 sample plots were meas- ured on productive forestland. Mainly due to computational limitations the sample plots were aggregated into 10 000 management units (1000 in each of 10 regions) by using cluster analyses.

Ten variables were used in the clustering proce- dure and they represent the explanatory variables in the diameter growth function, variables used for calculating logging costs, vegetation type and altitude.

The computations were done with the forestry scenario model Gaya-JLP. This model applies standard methodology (Johnson and Scheurman 1977, Garcia 1990, Siitonen 1993) of simulating treatment schedules (Gaya) for each management unit (Hoen and Eid 1990, Hoen and Gobakken 1997) and solving the management problem at forest level (JLP) by linear programming (Lappi 1992). Projections of the forest development, and the corresponding economic calculations, were provided by using a stand growth model

Table 1. Forest area in 10³ hectares and volume of growing stock in 10⁶ m³ grouped in site index classes and development-classes after aggregation into 10 000 management units.

Site quality class Development-class

(H40 – m) I II III IV V Sum %

Forest area (1000 ha)

6 16 39 25 180 376 635 10

8 87 287 70 450 490 1385 22

11 93 407 221 459 499 1678 26

14 83 389 289 236 289 1286 20

17 69 170 316 136 147 838 13

20 29 83 131 115 85 444 7

23 21 19 63 36 12 152 2

Sum 399 1395 1114 1612 1898 6418 100

% 6 22 17 25 30 100

Site quality class Development-class

(H40 – m) I II III IV V Sum %

Volume of growing stock (mill. m³)

6 0.00 0.00 0.66 11.62 33.77 46.05 7

8 0.00 0.00 3.33 36.41 59.30 99.03 16

11 0.00 0.30 11.67 52.35 87.12 151.44 25

14 0.00 0.77 21.20 39.32 71.87 133.16 22

17 0.00 2.72 33.45 26.81 39.36 102.34 17

20 0.00 0.90 14.93 21.67 20.23 57.72 9

23 0.00 0.47 9.95 8.64 4.53 23.60 4

Sum 0.00 5.16 95.19 196.81 316.18 613.34 100

% 0 1 15 32 52 100

Development-class: I – forest under regeneration, II – young forest, III – young thinning forest, IV – advanced thinning forest, V – mature forest

with the basal area mean diameter and mean height weighted by basal area as the basic enti- ties, and number of stems ha^–1 as a scaling factor.

Diameter increment functions (Blingsmo 1984), height development models (Tveite 1976, 1977, Braastad 1977) and a mortality model (Braastad 1982) drive the biological projections. Tree vol- umes are calculated by functions of Braastad (1966), Brantseg (1967) and Vestjordet (1967).

Timber (stumpage) values were estimated from gross price functions (Blingsmo and Veidahl 1992), and harvest costs from functions based on a tariff agreed upon by employers’ and employ- ees’ organisations (Overenskomst … 1996).

The price and cost level were chosen sub- jectively with the aim of refl ecting a realistic expectation of future (stumpage) prices and cor- responded roughly to an average of the prices in the period 1985–94 (Hoen et al. 1998a). Three levels of timber prices were applied, resulting in average gross prices (total for all species and qualities) of roughly 250 NOK m^–3, 325 NOK m^–3 and 400 NOK m^–3 (1 US$ = 8.96 NOK, August 2000). No relative changes for prices and costs over time were assumed, implying ^pr to be in real terms. Three levels of ^pr (1.5%, 2.5%

and 3.5%) were applied to study the sensitivity of this factor. The land expectation value of the ending inventory was estimated for each treat- ment schedule and included in the cash fl ow.

npv h c p

LEV p

ij ijt ijt r

tl t

t T

ijT r

T l

h

h

h

= − ⋅ +

+ ⋅ +

−

=

=

−

∑

( )

1 1

1 (1)

where npvij is the NPV of management unit i if assigned treatment schedule j, hijt and cijt are value of outputs and inputs, respectively, from period t, l is the number of years in each period, p_r is the required real rate of return pro anno, LEV_ijT

h is the land expectation value of manage- ment unit i as it reaches the planning horizon, denoted by Th, when assigned treatment schedule j. When calculating the LEV_ijT

h, i.e. the value of the ending inventory, predetermined treatment schedules, given for each dominating specie and varying with site index and p_r, were applied (Hoen 1990, Hoen and Gobakken 1997).

The planning horizon was 100 years, divided into 10 periods of equal length. Any treatments

were assumed to take place in the middle of each period. The following treatments were defi ned for the simulation:

1. Young growth tending

2. Thinning (one alternative for spruce and one for pine)

3. Establishment of seed-tree “stand” for pine 4. Establishment of shelterwood “stand” for spruce 5. Final felling

6. No treatment (“undisturbed growth”)

Final felling is always followed by regeneration of a new stand. For any stand two regeneration options were available, one “intensive” option involving planting and one “extensive” involving natural regeneration. Vegetation type was used to group the area into regeneration classes, assumed to represent good, moderate and diffi cult con- ditions for natural regeneration. A fourth type requires natural regeneration of spruce-dominated stands to be done by establishing a shelterwood

“stand”, and keeping it for a period of 20 years.

Two main features are used to specify the new stand, the regeneration lag and the tree number of each species. The regeneration lag as well as the tree number and species distribution varied with vegetation type, dominating tree specie and altitude. With spruce as the dominating specie, natural regeneration is assumed to be established by bordercuttings or small clearcuts, or by a shelterwood-procedure as explained above. For spruce the regeneration lag is set to 8, 14 and 20 years for the vegetation types classifi ed as good, moderate and diffi cult for natural regeneration.

Corresponding fi gures for broadleaf trees (birch) are 2, 5 and 8 years. Above a given altitude (600 metres above sea level in South-East Norway and 500 and 400 metres above sea level in West- ern and mid-Norway) the regeneration lag is increased by 10 years. With pine as the dominat- ing specie, natural regeneration is assumed done by retention of seed-trees, which are kept for 10–20 years. For pine the regeneration lag (the time from establishment of seed-trees until the new stand is established) is set to 5, 10 and 15 years, for altitudes below 300 metres above sea level, and 25, 30 and 35 years at higher altitudes.

The variation in the tree number and species dis- tribution is fairly modest among vegetation types

(±5%). For high-altitude forests, the tree number is reduced 20–40% compared with the lower alti- tudes. The establishment costs are appropriately varied for the “intensive” (4000–10 000 NOK/ha) and the “extensive” (0–1500 NOK/ha) regenera- tion alternative.

A priori feasibility requirements were specifi ed for each of the fi ve fi rst treatment options, while the 6^th (undisturbed growth) always would be feasible. It is crucial that the fi nal felling treatment is feasible over a fairly wide range of rotation ages, and an interval of 60–70 years around the anticipated economically effi cient (Faustmann) rotation age was applied. Within the limits of the feasibility requirements, all possible combina- tions of the treatments were simulated. In total for the 10 regions, 1 415 600, 1 345 861 and 1 282 363 treatment schedules were simulated for p_r of 1.5%, 2.5% and 3.5%, respectively. This means that each management unit in average was repre- sented by 128–142 different treatment schedules in the optimisation of the forest management problems. All forest management problems were solved at regional level, while the country level results were obtained by summing over the indi- vidual regions.

Three different management scenarios were analysed for each ^pr. In all problems the objec- tive function was maximisation of the NPV of the forest area. The fi rst Scenario I was a pure NPV maximisation (a Faustmann approach), while the second (Scenario II) included constraints guar- anteeing a non-declining felling path over time.

The third problem (Scenario III) restricted the fi rst period harvest not to exceed the “historic”

level and allowed a maximum change of ±10%

in harvested volume from any period to the fol- lowing.

Formally, the decision problems would consist of the objective function (2), the area-constraints (3), the non-negativity constraints (4) and eventu- ally some of the constraints (5)–(8):

maxz_p npv w

i n

ij ij

j J_i

= ⋅

= =

∑ ∑

(2)

s.t.

w_ij i

j J_i

= ∀

∑

, ⁽³⁾

w_ij≥0 for all and i j ⁽⁴⁾

ef w t T

ef uvol uvol

ijt ij ij

ijt ijt ijt

⋅ ≤ ∀ = −

= −

∑

+

0 1 2 1

1

, , ,...,

when ⁽⁵⁾

uvol_ij w_ij H

ij

1⋅ ≤

∑

uvol w uvol w

t T

ijt ij ijt ij

ij

⋅ ⋅ − ⋅ ≥

∀ = −

∑

1 2 1

. 1 ,

, ,...,

(7)

uvol w uvol w

t T

ijt ij ijt ij

ij

⋅ ⋅ − ⋅ ≤

∀ = −

∑

1 2 1

. 1 ,

, ,...,

(8)

symbols:

npvij the net present value of management unit i if assigned treatment schedule j

w_ij the weight (proportion) of management unit i assigned treatment schedule j

uvolijt the harvest volume in period t from man- agement unit i if assigned treatment sched- ule j. Thus ef_ijt is the difference in harvested volume between period t and t + 1.

H “historic” level of timber harvest, i.e. the harvested volume in the 10 years from 1983–1992

In Scenario II constraints (3), (4) and (5) were imposed, while Scenario III imposed constraints (3), (4), (6), (7) and (8). When none of the con- straints (5)–(8) are imposed, the best strategy will always be for each management unit i to apply the treatment schedule j that maximises the NPV. Then Scenario I reduces to picking the treatment schedule with the largest NPV for each management unit and may thus trivially be solved without being formulated as a LP-problem.

3 Results

The NPV of the forest area is presented in Table 2. For the two lowest p_r’s, there is a negligible drop in NPV when the non-declining felling path constraints are added (Scenario II) while for ^pr

of 3.5% the NPV drops with 2.2%, compared with the unconstrained problem (Scenario I). By imposing the constraints in Scenario III, the NPV is reduced by 1.8%, 5.6% and 12.4% for ^pr in ascending order. These fi gures represent estimates of the value of the intitial tree capital (growing stock), and the land it occupies, at different ^pr. Multiplying the NPV’s with p_r gives the theoreti- cal income (annual profi t) in real terms, which is found to be in the interval 2.7–2.8 · 10⁹ NOK for Scenario I and Scenario II, and 2.4–2.7 · 10⁹ NOK for Scenario III. Increasing p_r clearly reduces the annual profi t of Scenario III. In Scenario I (Scenario II) the total timber production (see Table 2 for defi nition) during the 100-year period increases by 15% (18%) when ^pr is lowered from 3.5% to 1.5%. In Scenario III the corresponding increase is 14%. All of the fi gures presenting timber volumes, are so-called ‘forest-volume’, i.e. the volume of the treetop, expected in-forest waste and losses, and bark are included. This typically amounts from 15%–25% of the total volume. The 0-area, i.e. forest area which is eco-

nomically non-accessible for timber production, were estimated to be roughly 6% of the produc- tive forest area. The four rows at the bottom of Table 2 presents results based on the theoretical assumption that the forest area was covered by a fully regulated forest with respect to the rota- tion ages specifi ed for estimating the value of the ending inventory. These fi gures resemble the steady state solution known from optimal control theory.

3.1 Timber Harvesting Potential and the Required Real Rate of Return (p_r) The results clearly demonstrate that the time- profi le of growing stock and timber harvesting are very sensitive to p_r. The potential annual harvests in the fi rst ten-year period were 13.2 · 10⁶ m³, 24.0 · 10⁶ m³ and 32.3 · 10⁶ m³, respectively, for p_r 1.5%, 2.5% and 3.5%. The low p_r (1.5%) gave a relatively low potential harvest at the start of the planning period, and a relatively high potential towards the end, while the high ^pr

(3.5%) gave a relatively high potential in the beginning, and a lower one towards the end.

The non-declining harvest path for the two fi rst 10-year periods increases with the ^pr, from 11.6 · 10⁶ m³ to 17.7 · 10⁶ m³ and 19.1 · 10⁶ m³, Table 2. NPV of the forest area, total timber production, productive forest area, 0-area and annual production and

growing stock in a fully regulated forest (explanation given in the text).

Required real rate of return, ^pr

Unit 1.5% 2.5% 3.5%

NPV in Scenario I 10⁹ · NOK 185.59 106.80 78.82

NPV in Scenario II 10⁹ · NOK 185.52 106.39 77.07

NPV in Scenario III 10⁹ · NOK 182.51 100.84 69.03

Total production in Scenario I 10⁶ · m³ 2201.03 2042.40 1920.10 Total production in Scenario II 10⁶ · m³ 2202.48 2019.08 1866.19 Total production in Scenario III 10⁶ · m³ 2190.58 2033.58 1922.63

Productive area 10⁵ · hectare 64.177 64.177 64.177

0-area 10⁵ · hectare 3.302 3.635 4.063

Fully Annual production from managed areas 10⁶ · m³ 20.81 19.25 18.58 regu- Annual production from 0-areas 10⁶ · m³ 0.68 0.74 0.84 lated Growing stock managed areas 10⁶ · m³ 688.59 579.11 507.00 forest Growing stock from 0-areas 10⁶ · m³ 20.25 23.12 21.49

Note: The total timber production over the planning horizon is defi ned as the sum of harvests in each period, plus the difference in growing stock between the time of inventory and the end of the 100-year-period. 0-areas, or economically non-accessible areas, are defi ned as management units for which all simulated treatment schedules have a NPV less than or equal to zero.

while the last period harvest is 23.8 · 10⁶ m³, 21.0 · 10⁶ m³ and 20.3 · 10⁶ m³. In Scenario III the harvest level constraints are binding from period 1 through 6 for the two highest ^pr, while they are binding in period 3–5 with p_r of 1.5%. The Fig. 2. Harvest paths for Scenario I and different p_r.

Fig. 3. Growing stock paths for Scenario I and different p_r.

Fig. 4. Harvest paths for Scenario II and different p_r.

Fig. 5. Growing stock paths for Scenario II and different p_r.

Fig. 6. Harvest paths for Scenario III and different p_r.

Fig. 7. Growing stock paths for Scenario III and dif- ferent p_r.

0 100 200 300

0 1 2 3 4 5 6 7 8 9 10

10-year period

1,5% 2,5% 3,5%

10⁶ · m³ o.b.

0 1 2 3 4 5 6 7 8 9 10

10-year period

1,5% 2,5% 3,5%

10⁶ · m³ o.b.

0 400 800 1200

0 100 200 300

0 1 2 3 4 5 6 7 8 9 10

10-year period

1,5% 2,5% 3,5%

10⁶ · m³ o.b.

0 1 2 3 4 5 6 7 8 9 10

10-year period

1,5% 2,5% 3,5%

10⁶ · m³ o.b.

0 400 800 1200

0 100 200 300

0 1 2 3 4 5 6 7 8 9 10

10-year period

1,5% 2,5% 3,5%

10⁶ · m³ o.b.

0 1 2 3 4 5 6 7 8 9 10

10-year period

1,5% 2,5% 3,5%

10⁶ · m³ o.b.

0 400 800 1200

time-profi les, or paths, for the periodic timber harvest and growing stock are presented in Figs.

2–7. The appendix presents the results in greater detail.

3.2 Intensity in Silvicultural Management, p_r and Timber Price Level

The intensity and extent of silvicultural man- agement applied on the forestland changes with

p_r. This can be verifi ed by inspecting the aver- age area assigned to the different silvicultural treatments as ^pr increases from 1.5% to 3.5%.

From Table 3 we see that the area assigned for fi nal-felling increases by roughly 30%, which is due to reduced rotation ages and more frequent harvesting. The area regenerated by planting is virtually unchanged, while the naturally regener- ated area increases by 30%. Thus, the proportion of natural regeneration increases. For the area being regenerated by planting, the reduction in rotation ages involve more frequent planting at the best sites, which just compensates for the increase in the marginal site quality class with planting as the most profi table regeneration option. The area treated by young growth tend- ing show a clear decrease. The area assigned to thinning and regeneration by retention of seed- or shelterwood-trees show a slight increase in absolute terms. The expenditures related to silvi- cultural management decrease by nearly 35%, supporting the claim that the intensity in silvicul- tural management will decrease as ^pr increase.

At the highest ^pr the area planted and thinned

is clearly higher in Scenario II than in Scenario I. This relates to the non-declining harvest path constraint, as more planting and thinning makes feasible a larger immediate harvest.

Changes in the permanent price-level of timber also impact the timber management strategies in the expected way. A reduction in timber prices will decrease the profi tability of silvicultural investments and thus reduce e.g. areas regener- ated by planting or treated by young growth tend- ing. On the part of the forest area where some silvicultural investments are done, a decrease in timber prices will change the ratio between output-prices and input-costs. This will have two effects; i) the intensity in silvicultural manage- ment will decrease, ii) the value of forestland and thus the soil rent will decrease, implying the optimal rotation age to increase. Both effects will reduce the activity in terms of average plant- ing expenditures and average area planted. The results presented in Table 4 supports these claims.

The proportion of the area established by planting after fi nal felling is reduced from 34% to 27%, while the area treated by young growth tending decrease by 21% when timber price changes from the “high” to the “low” level. The expenditures related to silvicultural management decrease by 31%.

Table 3. Average area in 1000 hectare per 10-year period assigned different treatments and average expenditures in silvicultural treatments in 10⁶ NOK per 10-year period for Scenario I. Values for Scenario II and Scenario III are given as percentage of Scenario I for the corresponding p_r.

Area assigned different treatments

p_r No trt. Planting Nat.regen. Y.gr.tend. Thinning Seed-/sh. Final-felling Silv.exp.

Scenario I 1.5% 5345.4 179.9 341.5 323.9 66.3 160.7 481.5 1600.6 Scenario II 1.5% 100.1 99.8 100.2 99.0 97.3 100.5 100.1 99.7 Scenario III 1.5% 101.8 90.6 88.8 94.2 89.9 90.9 88.6 91.0 Scenario I 2.5% 5261.5 182.8 432.7 290.0 81.9 168.9 575.5 1315.5 Scenario II 2.5% 99.7 102.1 101.2 100.0 103.5 101.9 101.6 101.3 Scenario III 2.5% 103.3 89.5 82.3 89.6 65.7 87.3 83.3 88.5 Scenario I 3.5% 5287.8 182.7 466.6 216.0 87.7 177.0 609.4 1059.3 Scenario II 3.5% 98.3 111.1 104.8 99.3 140.4 108.3 107.0 107.3 Scenario III 3.5% 104.0 89.8 80.1 83.0 59.2 85.6 81.7 87.3

Note: Explanation of column titles: No trt.: No treatment, Nat.regen: natural regeneration, Y.gr.tend.: Young growth tending, Seed-/sh.: Establishment of seed-tree and shelter-wood stands, Silv.exp.: Silvicultural expenditures.

3.3 Cash Flow, Capital Accumulation and Capital Yields

Table 5 present the cash fl ow’s for the three levels of p_r. Naturally, there is a close connection between the time-profi le of the timber harvest and the cash fl ow. In Scenario I, the fi rst period cash fl ow is roughly 2.5 times larger when p_rof 3.5% is compared with 1.5%. From period 3 and through the rest of the 100-year period, the lowest p_r generates the largest cash fl ow from the forest area. This relate to the basic fact that the lower p_r the more attractive will capital investments in silvicultural management and accumulation of growing stock be. Over time this will lead to a larger production of timber in absolute terms as long as rotation ages don’t exceed the maximum

sustainable yield rotation (i.e. the rotation age when marginal and average growth equals). The last row in Table 5 gives the NPV, when the cash fl ows from the forest area managed accord- ing to ^pr of 1.5%, 2.5% and 3.5% respectively, are valued with a p_r of 3.5%. Comparing these NPV’s may give an estimate of the renounced capital value, if the forest is managed according to a lower ^pr than what may actually be obtain- able in alternative projects or the capital market.

This may be a quite plausible situation, e.g. due to effects of the tax system. Let us assume that the forest area is managed according to a p_r of 1.5%, while the capital market yields 3.5%.

Thus, the capital yield (released profi t) from the forest area may be invested outside the forest and thus obtain an annual real rate of return of 3.5%.

Table 4. Average area in 1000 hectare per 10-year period assigned different treatments and average expenditures in silvicultural treatments in 10⁶ NOK per 10-year period for Scenario I with different timber prices. Values for Scenario II are given as percentage of Scenario I for the corresponding price-level. p_r = 2.5%.

Area assigned different treatments

Price No trt. Planting Nat.regen. Y.gr.tend. Thinning Seed-/sh. Final-felling Silv.exp.

Scenario I high 5174.8 227.8 435.0 317.0 92.4 170.7 622.9 1562.6 Scenario II high 99.4 102.0 101.1 101.3 109.3 104.8 101.5 101.2 Scenario I medium 5261.5 182.8 432.7 290.0 81.9 168.9 575.5 1315.5 Scenario II medium 99.7 102.1 101.2 100.0 103.5 101.9 101.6 101.3 Scenario I low 5402.6 144.3 395.4 252.1 63.1 160.2 499.8 1080.7 Scenario II low 99.8 101.4 100.5 99.3 105.7 101.8 100.8 100.7

Note: Explanation of column titles: No trt.: No treatment, Nat.regen: natural regeneration, Y.gr.tend.: Young growth tending, Seed-/sh.: Establishment of seed-tree and shelter-wood stands, Silv.exp.: Silvicultural expenditures.

Fig. 9. Growing stock paths for Scenario II and different price levels. p_r = 2.5%.

Fig. 8. Harvest paths for Scenario II and different price levels. p_r = 2.5%.

0 100 200 300

0 1 2 3 4 5 6 7 8 9 10

10-year period

Low prices Medium prices High prices

10⁶ · m³ o.b.

0 1 2 3 4 5 6 7 8 9 10

10-year period 10⁶ · m³ o.b.

0 400 800 1200

Low prices Medium prices High prices

Comparing the fi gures of column four and two (Scenario I) in the last row of Table 5 gives the difference in NPV of 13.4 · 10⁹ NOK or 17%.

The harvest path with 1.5% p_r in Scenario II and Scenario III has a gradual increase over the planning period, different from Scenario I with the same p_r. The difference in NPV for e.g.

Scenario III (column four and eight of Table 5) is 17.2 · 10⁹ NOK equivalent to an annual theoreti- cal income of 0.6 · 10⁹ NOK. This estimate com- prises the combined effect of 1) harvest path constraints and 2) design of forest management at an inapproriate required real rate of return, on the contributing profi t from the forest area.

4 Discussion

The aim of the analyses has been to map the timber production possibilities of the productive forest area of Norway and how it relates to the p_r. In general, the results correspond well to intuitive reasoning based on forest economic theory.

4.1 Data and Empirical Models

The analyses have been accomplished within a frame of objective criteria and long empirical

experience. They were based on a large and rep- resentative data set describing the productive forest area of Norway. The number of manage- ment units was considerably larger than in earlier studies done in Norway (Nersten et al. 1981, Klargjøring av … 1999). The moderate aggrega- tion of sample plots was done in a way that secured a minimum loss of information for the selected cluster variables (e.g. Eriksson 1983, Hoen 1996, Weintraub et al. 1997). The cluster variables included biological state variables as well as economically related variables like terrain accessibility and terrain transportation distance.

The large number of management units and the method used for aggregation provided for a broad variation of treatment schedules, i.e. a compre- hensive decision-space. This is believed to be par- ticularly important in analyses pretending to map the sensitivity of the timber production potential to changes in the ^pr. The treatment options that were eligible when simulating treatment schedules cover the most relevant and frequently applied silvicultural treatments in Norway, see Hoen et al.

(1998a) for details.

The analysis tool (Gaya-JLP) builds on a long tradition of development and application of com- prehensive models for long-range timber produc- tion analyses in Norway and in the other Nordic countries, cf. e.g. Eid and Hobbelstad (2000) in Norway, Eriksson (1983) and Lundström and Table 5. Net cash fl ow from the forest area per 10-year period and net present value of future cash fl ow at time

0 (NPV0) and 100 (NPV100). Figures in 10⁹ NOK.

Scenario I Scenario II Scenario III

p_r p_r p_r

10-year period 1.5% 2.5% 3.5% 1.5% 2.5% 3.5% 1.5% 2.5% 3.5%

1 18.1 35.2 45.6 15.8 27.1 30.7 15.8 19.7 21.0

2 12.8 17.5 15.8 17.6 24.7 26.3 18.2 20.7 21.7

3 22.2 21.4 20.4 21.2 24.1 24.6 20.5 22.3 22.8

4 28.7 26.8 24.4 28.8 25.1 26.0 23.1 24.7 25.0

5 32.1 27.9 16.0 29.6 27.1 24.9 25.8 27.5 27.8

6 36.3 21.9 21.7 33.2 27.4 26.6 29.0 30.7 28.8

7 33.4 24.0 21.1 33.4 28.6 25.2 30.7 30.3 30.9

8 27.0 30.9 26.2 33.2 30.1 23.6 33.3 32.3 30.9

9 37.2 35.8 22.3 35.9 30.7 22.7 36.1 32.7 29.4

10 39.1 25.9 19.2 39.1 28.7 20.1 35.9 31.0 26.9

NPV0 185.6 106.8 78.8 185.5 106.4 77.1 182.5 100.8 69.0 NPV100in 231.6 111.9 68.32 230.6 104.8 48.6 234.8 117.6 69.7 NPV0 at p_r3.5% 65.4 76.8 78.8 65.3 75.7 77.1 61.6 67.5 69.0

Söderberg (1996) in Sweden and Lappi (1992) and Siitonen (1993) in Finland. Empirically based stand growth and timber valuation sub-models were applied to calculate alternative treatment schedules for each management unit. The largest uncertain- ties were related to (i) assumptions for regeneration of forest stands, (ii) modelling of tree mortality and (iii) limited possibilities for simulating silvicultural practices based on selective cutting.

Among the set of assumptions defi ning regener- ation-options, establishment of new forests based on natural regeneration were particularly burdened with uncertainty. Any bias in the assumptions for natural regeneration will infl uence the choice of regeneration method, while the resulting bias on timber production affects growing stock and har- vesting potentials in a fairly distant future. Mortal- ity was modelled as a fi xed proportion of the number of trees (Braastad 1982) in established stands (i.e. dominant height above 9 metres), and this might be especially critical for strategies involving substantial extension of the rotation age.

The longest rotation ages are applied in Scenario III (all ^pr) and for Scenario I and Scenario II with p_r of 1.5%. Assuming a larger mortality in old forest would reduce the net growth and the harvesting potential, which in turn would reduce the NPV of these strategies. A silvicultural regime based on selective cuttings was approximated for high-elevation forests. This involved two consecu- tive thinnings before fi nal felling, and then a new stand was assumed established in the next 10-year period with an age of about 50 years. Better solu- tions would be possible, however, if single-tree growth models, similar to those used in HUGIN in Sweden (Söderberg 1986) or MELA in Fin- land (Hynynen 1995, Siitonen et al. 1996), could be implemented (Nersten 1997). This would also facilitate the specifi cation of silvicultural regimes based on all-age management or selective cuttings for the whole forest area.

When estimated growth was compared to actual growth based on tree ring measurements on the NFI-plots, the growth estimated for the fi rst 5 years by the GAYA-model was found to be 7–8% lower than the measured growth. This is not considered to be critical for the conclusion of this study.

Even if there should be biases in the estimation of production potentials, the differences between alternatives, and thus the relative impact of chang-

ing e.g. p_r or the timber price level, are believed to be reasonably consistent and unbiased.

4.2 The Decision Model

A straightforward decision model is applied, with the objective of maximising the NPV of the forest area. The NPV was calculated within the Faust- mann-tradition. It is implicitly assumed that the management units can be treated independently, since output is a linear function of the area assigned to the treatment schedules for each management unit. This also implies that any quantity of timber could be sold without affecting the price-level of timber, which is obviously a simplistic assump- tion. Applying downward-sloping demand would tend to smooth the harvest path through time and thus bring the solution to Scenario I closer to that of Scenario II or Scenario III. Imports of pulpwood to Norway have been signifi cant during the last 30 years, indicating that the Nor- wegian round-wood market is closely linked to the international. Thus, the world-market price of round-wood, adjusted for transportation costs, can be regarded as a price-fl oor/-ceiling for the domestic round-wood price. In this perspective the price-taker assumption is more defensible.

4.3 Comparison with Other Studies

There are several examples of national or regional analyses based on a representative sample of the productive forest area with focus on timber pro- duction carried out in the Nordic countries (e.g.

Nersten et al. 1981, Hofstad 1991, Skogspolitiken inför … 1992 and Siitonen and Nuutinen 1996).

Given the differences in methodology and the way of specifying assumptions for silvicultural manage- ment and biological development, the results from the present study conform well to what Nersten et al. (1981) obtained. Hofstad’s (1991) “steady state” results conform quite well to comparable results in this study with p_r of 1.5% (Table 2). For the higher ^pr there are signifi cant differences, as Hofstad’s (1991) results imply much lower levels of harvest and growing stock. One explanation may be that the function estimating forest volume differs from the growth model applied in this study.

Hofstad’s (1991) logistic function is not capable of adjusting growth according to the age-structure of the forest, as the growth model in Gaya does.

Assuming that volume growth and profi tability of timber production decrease with age over the rel- evant range of rotation ages, Hofstad’s model may, compared with Gaya, underestimate the marginal growth rate and profi tability of timber production when the growing stock is relatively small. With Gaya a small level of growing stock will imply a relatively young forest and thus a high annual growth, a high marginal growth rate and a relatively high marginal profi tability of extending the rotation age.

4.4 Non-timber Outputs

The forest area in Norway provides a large variety of outputs in addition to timber. As pointed out by Hofstad (1991), concerns related to the provi- sion of non-timber outputs signifi cantly affect forest management practices. The general trend is that non-timber concerns in the short-run reduce harvest-levels and thus increase levels of growing stock. In the long run this will lead to increased removals, either by harvests or natural mortality, and possibly temporarily to lower growing stocks than if less constraints were imposed initially. The impact of some selected environmentally oriented constraints, using the same data and model as this study, is analysed by Hoen et al. (1998b).

4.5 Policy Implications

In 1997–98 the Ministry of Agriculture in Norway prepared a report to the Parliament on the forest policy. The report was presented to the Parliament in Dec. 1998 and was discussed in the Parlia- ment in May–June 1999. The report represented a departure from tradition, as no explicit target was proposed for the desired level of future timber harvests. Neither was any quantitative fi gures presented in the report, showing possible conse- quences of different policies as regards e.g. the level of intensity in silvicultural investments. The fi ndings presented in this paper were provided to the Ministry of Agriculture while the report to the Parliament was in preparation. The observa-

tion made by Hofstad (1991) that “Forest econo- mists also have pointed at the connection between harvest, inventory and the social discount rate (Svendsrud 1988), without really being able to bring the point home to policy makers” (bold characters added) remain valid and may still be repeated.

The growing stock represents a huge capital.

The growth-rate of this timber volume, a key indicator in evaluating the rate of return obtained from this capital, is in the range of 1.5–2.5% pro anno for the oldest part of the forest (Statistics of

… 2000). If we assume that the stumpage price of timber will follow the general price level (CPI), then this growth-rate will constitute a sound indi- cator of the real rate of return obtained by hold- ing capital in old forest. The key question is whether this rate of return is satisfactory, or if more attractive alternative investments, yielding higher real rates of return, exist. Consideration of, and attitudes towards, risk will be crucial in this setting. Despite the apparent size of potential losses in capital yield, these questions were not addressed or discussed explicitly in the recent Report to the Parliament on the forest policy prepared by the Ministry of Agriculture.

5 Conclusions

The analyses confi rm that the timber production possibilities, and the corresponding time-profi le of timber harvests and growing stock, heavily depend on the chosen p_r. In Norway, the current state of the productive forest area provides a solid basis for timber production far into this century.

The non-declining harvest path (Scenario II) is, compared with a historic level of timber harvests, estimated to be 50–60% larger for the fi rst three 10-year periods and it increases further to be roughly 70% above the historic level given the p_r of 2.5% and 3.5%. The harvest potential with p_r of 1.5%, equals the historic level for the fi rst two 10-year periods, while it is increasing dramati- cally to twice the historic level by the end of the planning horizon. The harvest paths of Scenario III, when harvests are restricted not to exceed the “historic” level in period 1 and allowed to fl uctuate ±10% from period to period, are almost

identical for all p_r and show a steady increase throughout the whole planning period. These har- vest paths (Figs. 6 and 7) are accompanied by an increasing growing stock, most pronounced and persistent for the lowest p_r. If we adjust for the differences in total harvest through the planning period, the growing stock increases by 99.5 · 10⁶ m³ (242.7 · 10⁶ m³) when p_r decrease from 3.5% to 2.5% (1.5%). These differences may be attributable to changes in optimal silvi- cultural management as the p_r changes. These results uniformly affi rm, that if not the removal increases drastically from the historic level, either by harvest or by natural mortality, the growing stock will continue to increase.

Acknowledgements

This article is based on work done in a project fi nancially supported by the Norwegian Research Council and the project Living Forests through the project “Economic consequences of measures for more sustainable forestry” (NFR-110 407/110) and by the Norwegian Forest Research Institute.

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